// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_PARAMETRIZEDLINE_H
#define EIGEN_PARAMETRIZEDLINE_H

namespace Eigen {

/** \geometry_module \ingroup Geometry_Module
  *
  * \class ParametrizedLine
  *
  * \brief A parametrized line
  *
  * A parametrized line is defined by an origin point \f$ \mathbf{o} \f$ and a unit
  * direction vector \f$ \mathbf{d} \f$ such that the line corresponds to
  * the set \f$ l(t) = \mathbf{o} + t \mathbf{d} \f$, \f$ t \in \mathbf{R} \f$.
  *
  * \tparam _Scalar the scalar type, i.e., the type of the coefficients
  * \tparam _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
  */
template <typename _Scalar, int _AmbientDim, int _Options> class ParametrizedLine
{
public:
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar, _AmbientDim)
    enum
    {
        AmbientDimAtCompileTime = _AmbientDim,
        Options = _Options
    };
    typedef _Scalar Scalar;
    typedef typename NumTraits<Scalar>::Real RealScalar;
    typedef Eigen::Index Index;  ///< \deprecated since Eigen 3.3
    typedef Matrix<Scalar, AmbientDimAtCompileTime, 1, Options> VectorType;

    /** Default constructor without initialization */
    EIGEN_DEVICE_FUNC inline ParametrizedLine() {}

    template <int OtherOptions>
    EIGEN_DEVICE_FUNC ParametrizedLine(const ParametrizedLine<Scalar, AmbientDimAtCompileTime, OtherOptions>& other)
        : m_origin(other.origin()), m_direction(other.direction())
    {
    }

    /** Constructs a dynamic-size line with \a _dim the dimension
    * of the ambient space */
    EIGEN_DEVICE_FUNC inline explicit ParametrizedLine(Index _dim) : m_origin(_dim), m_direction(_dim) {}

    /** Initializes a parametrized line of direction \a direction and origin \a origin.
    * \warning the vector direction is assumed to be normalized.
    */
    EIGEN_DEVICE_FUNC ParametrizedLine(const VectorType& origin, const VectorType& direction) : m_origin(origin), m_direction(direction) {}

    template <int OtherOptions> EIGEN_DEVICE_FUNC explicit ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane);

    /** Constructs a parametrized line going from \a p0 to \a p1. */
    EIGEN_DEVICE_FUNC static inline ParametrizedLine Through(const VectorType& p0, const VectorType& p1)
    {
        return ParametrizedLine(p0, (p1 - p0).normalized());
    }

    EIGEN_DEVICE_FUNC ~ParametrizedLine() {}

    /** \returns the dimension in which the line holds */
    EIGEN_DEVICE_FUNC inline Index dim() const { return m_direction.size(); }

    EIGEN_DEVICE_FUNC const VectorType& origin() const { return m_origin; }
    EIGEN_DEVICE_FUNC VectorType& origin() { return m_origin; }

    EIGEN_DEVICE_FUNC const VectorType& direction() const { return m_direction; }
    EIGEN_DEVICE_FUNC VectorType& direction() { return m_direction; }

    /** \returns the squared distance of a point \a p to its projection onto the line \c *this.
    * \sa distance()
    */
    EIGEN_DEVICE_FUNC RealScalar squaredDistance(const VectorType& p) const
    {
        VectorType diff = p - origin();
        return (diff - direction().dot(diff) * direction()).squaredNorm();
    }
    /** \returns the distance of a point \a p to its projection onto the line \c *this.
    * \sa squaredDistance()
    */
    EIGEN_DEVICE_FUNC RealScalar distance(const VectorType& p) const { EIGEN_USING_STD(sqrt) return sqrt(squaredDistance(p)); }

    /** \returns the projection of a point \a p onto the line \c *this. */
    EIGEN_DEVICE_FUNC VectorType projection(const VectorType& p) const { return origin() + direction().dot(p - origin()) * direction(); }

    EIGEN_DEVICE_FUNC VectorType pointAt(const Scalar& t) const;

    template <int OtherOptions> EIGEN_DEVICE_FUNC Scalar intersectionParameter(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;

    template <int OtherOptions> EIGEN_DEVICE_FUNC Scalar intersection(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;

    template <int OtherOptions> EIGEN_DEVICE_FUNC VectorType intersectionPoint(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;

    /** Applies the transformation matrix \a mat to \c *this and returns a reference to \c *this.
    *
    * \param mat the Dim x Dim transformation matrix
    * \param traits specifies whether the matrix \a mat represents an #Isometry
    *               or a more generic #Affine transformation. The default is #Affine.
    */
    template <typename XprType> EIGEN_DEVICE_FUNC inline ParametrizedLine& transform(const MatrixBase<XprType>& mat, TransformTraits traits = Affine)
    {
        if (traits == Affine)
            direction() = (mat * direction()).normalized();
        else if (traits == Isometry)
            direction() = mat * direction();
        else
        {
            eigen_assert(0 && "invalid traits value in ParametrizedLine::transform()");
        }
        origin() = mat * origin();
        return *this;
    }

    /** Applies the transformation \a t to \c *this and returns a reference to \c *this.
    *
    * \param t the transformation of dimension Dim
    * \param traits specifies whether the transformation \a t represents an #Isometry
    *               or a more generic #Affine transformation. The default is #Affine.
    *               Other kind of transformations are not supported.
    */
    template <int TrOptions>
    EIGEN_DEVICE_FUNC inline ParametrizedLine& transform(const Transform<Scalar, AmbientDimAtCompileTime, Affine, TrOptions>& t,
                                                         TransformTraits traits = Affine)
    {
        transform(t.linear(), traits);
        origin() += t.translation();
        return *this;
    }

    /** \returns \c *this with scalar type casted to \a NewScalarType
    *
    * Note that if \a NewScalarType is equal to the current scalar type of \c *this
    * then this function smartly returns a const reference to \c *this.
    */
    template <typename NewScalarType>
    EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<ParametrizedLine, ParametrizedLine<NewScalarType, AmbientDimAtCompileTime, Options>>::type
    cast() const
    {
        return typename internal::cast_return_type<ParametrizedLine, ParametrizedLine<NewScalarType, AmbientDimAtCompileTime, Options>>::type(*this);
    }

    /** Copy constructor with scalar type conversion */
    template <typename OtherScalarType, int OtherOptions>
    EIGEN_DEVICE_FUNC inline explicit ParametrizedLine(const ParametrizedLine<OtherScalarType, AmbientDimAtCompileTime, OtherOptions>& other)
    {
        m_origin = other.origin().template cast<Scalar>();
        m_direction = other.direction().template cast<Scalar>();
    }

    /** \returns \c true if \c *this is approximately equal to \a other, within the precision
    * determined by \a prec.
    *
    * \sa MatrixBase::isApprox() */
    EIGEN_DEVICE_FUNC bool isApprox(const ParametrizedLine& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
    {
        return m_origin.isApprox(other.m_origin, prec) && m_direction.isApprox(other.m_direction, prec);
    }

protected:
    VectorType m_origin, m_direction;
};

/** Constructs a parametrized line from a 2D hyperplane
  *
  * \warning the ambient space must have dimension 2 such that the hyperplane actually describes a line
  */
template <typename _Scalar, int _AmbientDim, int _Options>
template <int OtherOptions>
EIGEN_DEVICE_FUNC inline ParametrizedLine<_Scalar, _AmbientDim, _Options>::ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane)
{
    EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
    direction() = hyperplane.normal().unitOrthogonal();
    origin() = -hyperplane.normal() * hyperplane.offset();
}

/** \returns the point at \a t along this line
  */
template <typename _Scalar, int _AmbientDim, int _Options>
EIGEN_DEVICE_FUNC inline typename ParametrizedLine<_Scalar, _AmbientDim, _Options>::VectorType
ParametrizedLine<_Scalar, _AmbientDim, _Options>::pointAt(const _Scalar& t) const
{
    return origin() + (direction() * t);
}

/** \returns the parameter value of the intersection between \c *this and the given \a hyperplane
  */
template <typename _Scalar, int _AmbientDim, int _Options>
template <int OtherOptions>
EIGEN_DEVICE_FUNC inline _Scalar
ParametrizedLine<_Scalar, _AmbientDim, _Options>::intersectionParameter(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const
{
    return -(hyperplane.offset() + hyperplane.normal().dot(origin())) / hyperplane.normal().dot(direction());
}

/** \deprecated use intersectionParameter()
  * \returns the parameter value of the intersection between \c *this and the given \a hyperplane
  */
template <typename _Scalar, int _AmbientDim, int _Options>
template <int OtherOptions>
EIGEN_DEVICE_FUNC inline _Scalar
ParametrizedLine<_Scalar, _AmbientDim, _Options>::intersection(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const
{
    return intersectionParameter(hyperplane);
}

/** \returns the point of the intersection between \c *this and the given hyperplane
  */
template <typename _Scalar, int _AmbientDim, int _Options>
template <int OtherOptions>
EIGEN_DEVICE_FUNC inline typename ParametrizedLine<_Scalar, _AmbientDim, _Options>::VectorType
ParametrizedLine<_Scalar, _AmbientDim, _Options>::intersectionPoint(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const
{
    return pointAt(intersectionParameter(hyperplane));
}

}  // end namespace Eigen

#endif  // EIGEN_PARAMETRIZEDLINE_H
